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5.8 Explain how the following conditions can be represented as linear constraints using binary variables. (a)...

5.8 Explain how the following conditions can be represented as linear constraints using binary variables. (a) Either x1 + x2 ? 3 or 3x1 + 4x2 ? 10 (b) Variable x2 can assume values 0, 4, 7, 10, and 12 only (c) If x2 ? 3, then x3 ? 6; Otherwise x3 ? 4 (assume x2 and x3 are integers) (d) At least 2 out of the following 5 constraints must be satisfied:

x1 + x2 <=7

x1 ? x2 >=3

2x1 + 3x2 <=20

4x1 ? 3x2 >=10

x2 ? 6

x1, x2 ? 0

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